919 research outputs found
Unified treatment of the Coulomb and harmonic oscillator potentials in dimensions
Quantum mechanical models and practical calculations often rely on some
exactly solvable models like the Coulomb and the harmonic oscillator
potentials. The dimensional generalized Coulomb potential contains these
potentials as limiting cases, thus it establishes a continuous link between the
Coulomb and harmonic oscillator potentials in various dimensions. We present
results which are necessary for the utilization of this potential as a model
and practical reference problem for quantum mechanical calculations. We define
a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate
the Green's operator on this basis and also present an SU(1,1) algebra
associated with it. We formulate the problem for the one-dimensional case too,
and point out that the complications arising due to the singularity of the
one-dimensional Coulomb problem can be avoided with the use of the generalized
Coulomb potential.Comment: 18 pages, 3 ps figures, revte
Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
We study the one-dimensional Dirac equation with local PT-symmetric
potentials whose discrete eigenfunctions and continuum asymptotic
eigenfunctions are eigenfunctions of the PT operator, too: on these conditions
the bound-state spectra are real and the potentials are reflectionless and
conserve unitarity in the scattering process. Absence of reflection makes it
meaningful to consider also PT-symmetric potentials that do not vanish
asymptotically.Comment: 24 pages, to appear in J. Phys. A : Math. Theor; one acknowledgement
and one reference adde
Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal
(Jacobi) matrix form in some discrete Hilbert-space basis representation, then
its Green's operator can be constructed in terms of a continued fraction. As an
illustrative example we discuss the Coulomb Green's operator in
Coulomb-Sturmian basis representation. Based on this representation, a quantum
mechanical approximation method for solving Lippmann-Schwinger integral
equations can be established, which is equally applicable for bound-, resonant-
and scattering-state problems with free and Coulombic asymptotics as well. The
performance of this technique is illustrated with a detailed investigation of a
nuclear potential describing the interaction of two particles.Comment: 7 pages, 4 ps figures, revised versio
Parton coalescence and antiproton/pion anomaly at RHIC
Coalescence of minijet partons with the partons from the quark-gluon plasma
formed in relativistic heavy ion collisions is suggested as the mechanism for
production of hadrons with intermediate transverse momentum. The resulting
enhanced antiproton and pion yields at intermediate transverse momentum gives a
plausible explanation for the observed large antiproton to pion ratio. With
further increasing momentum, the ratio is predicted to decrease and approach
the small value given by independent fragmentations of minijet partons after
their energy loss in the quark-gluon plasma.Comment: 4 pages, 3 figures, version to appear in Phys. Rev. Let
Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the
complex domain, to a number of complex Hamiltonians, characterized by discrete
parity and time reversal (PT) symmetries and obtain their eigenvalues and
eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials
are analyzed and the subtle differences, in the singularity structures of their
quantum momentum functions, are pointed out. The role of the PT symmetry in the
complex domain is also illustrated.Comment: 11 page
Jet Tomography in the Forward Direction at RHIC
Hadron production at high- displays a strong suppression pattern in a
wide rapidity region in heavy ion collisions at RHIC energies. This finding
indicates the presence of strong final state effects for both transversally and
longitudinally traveling partons, namely induced energy loss. We have developed
a perturbative QCD based model to describe hadron production in collision,
which can be combined with the Glauber -- Gribov model to describe hadron
production in heavy ion collisions. Investigating and collisions
at energy GeV at mid-rapidity, we find the opacity of the
strongly interacting hot matter to be proportional to the participant nucleon
number. Considering forward rapidities, the suppression pattern indicates the
formation of a longitudinally contracted dense deconfined zone in central heavy
ion collisions. We determine parameters for the initial geometry from the
existing data.Comment: 6 pages for Hot Quarks '06 Conferenc
Generalized Swanson models and their solutions
We analyze a class of non-Hermitian quadratic Hamiltonians, which are of the
form , where are real constants, with , and and are generalized
creation and annihilation operators. Thus these Hamiltonians may be classified
as generalized Swanson models. It is shown that the eigenenergies are real for
a certain range of values of the parameters. A similarity transformation
, mapping the non-Hermitian Hamiltonian to a Hermitian one , is
also obtained. It is shown that and share identical energies. As
explicit examples, the solutions of a couple of models based on the
trigonometric Rosen-Morse I and the hyperbolic Rosen-Morse II type potentials
are obtained. We also study the case when the non-Hermitian Hamiltonian is
symmetric.Comment: 17 page
Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
We develop a systematic approach to construct novel completely solvable
rational potentials. Second-order supersymmetric quantum mechanics dictates the
latter to be isospectral to some well-studied quantum systems.
symmetry may facilitate reconciling our approach to the requirement that the
rationally-extended potentials be singularity free. Some examples are shown.Comment: 13 pages, no figure, some additions to introduction and conclusion, 4
more references; to be published in Special issue of Pramana - J. Phy
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